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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
I Introduction
1.1. Introductory remarks.................................................. 5
1.2. Baire spaces............................................................... 6
1.3. Completeness properties......................................... 8
1.4. Conventions................................................................. 9
II. Global completeness
2.1. The global completeness properties..................... 11
2.2. Products and subspaces.......................................... 13
2.3. Mappings...................................................................... 15
2.4. Examples..................................................................... 17
III. Moore spaces
3.1. Moore completeness and Rudin completeness............................... 20
3.2. Countable global completeness in Moore spaces........................... 21
3.3. Moore spaces and Baire spaces......................................................... 24
IV. Local and almost completeness
4.1. Dense complete subspaces................................................................. 20
4.2. Products and subspaccs.................................................................................... 28
4.3. Mappings................................................................................................................ 30
V. Additional remarks
5.1. Miscellaneous topics.............................................................................. 34
5.2. Relations between the completeness properties............................. 37
5.3. Open problems........................................................................................ 40
References.................................................................................................................... 42
I Introduction
1.1. Introductory remarks.................................................. 5
1.2. Baire spaces............................................................... 6
1.3. Completeness properties......................................... 8
1.4. Conventions................................................................. 9
II. Global completeness
2.1. The global completeness properties..................... 11
2.2. Products and subspaces.......................................... 13
2.3. Mappings...................................................................... 15
2.4. Examples..................................................................... 17
III. Moore spaces
3.1. Moore completeness and Rudin completeness............................... 20
3.2. Countable global completeness in Moore spaces........................... 21
3.3. Moore spaces and Baire spaces......................................................... 24
IV. Local and almost completeness
4.1. Dense complete subspaces................................................................. 20
4.2. Products and subspaccs.................................................................................... 28
4.3. Mappings................................................................................................................ 30
V. Additional remarks
5.1. Miscellaneous topics.............................................................................. 34
5.2. Relations between the completeness properties............................. 37
5.3. Open problems........................................................................................ 40
References.................................................................................................................... 42
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
116
Liczba stron
43
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom 116
Daty
wydano
1974
Twórcy
autor
- Delft Institute of Technology, Delft, Netherlands
autor
- University of Pittsburgh, Pittsburgh, Pa., 15260, U. S. A.
Bibliografia
- [1] J. M. Aarts, Notes of Colloquium Cotopology, Mathematical Centre, Amsterdam 1965.
- [2] J. M. Aarts, Cocompactifications, Indag. Math. 32 (1970), pp. 9-21.
- [3] J. M. Aarts, Semi-proximity spaces and cocompactness, I and II, Indag. Math. 32 (1970), pp. 403-427.
- [4] J. M. Aarts, J. de Groot and R. H. McDowell, Cocompactness, Nieuw Arch. Wish. 18 (1970), pp. 2-15.
- [5] J. M. Aarts, J. de Groot and R. H. McDowell, Cotopology for metrizable spaces, Duke Math. J. 37 (1970), pp. 291-295.
- [6] J. M. Aarts, D. J. Lutzer, The product of totally nonmeagre spaces, Proc. Amer. Math. Soc. 38 (1973), pp. 198-200.
- [7] J. M. Aarts, D. J. Lutzer, Pseudo-completeness and the product of Baire spaces, Pacific J. Math. 48 (1973), pp. 1-10.
- [8] R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), pp. 175-186.
- [9] C. J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), pp. 1-16.
- [10] N. Bourbaki, Elements of Mathematics: General Topology, Part 2, Reading, Mass. 1966.
- [11] E. Čech, On bicompact spaces, Ann. of Math. 38 (1937), pp. 823-844.
- [12] G. Choquet, Une classe régulière d'espaces de Baire, C. R. Acad. Sci. Paris, Série A, 246 (1958), pp. 218-220.
- [13] G. Choquet, Lectures on Analysis, Volume 1, New York 1969.
- [14] W. W. Comfort, Functions linearly continuous on a product of Baire spaces, Boll. Un. Mat. Ital. 20 (1965), pp. 128-134.
- [15] W. W. Comfort and S. Negrepontis, The ring С (X) determines the category of X, Proc. Amer. Math. Soc. 16 (1965), pp. 1041-1045.
- [16] J. Chaber, M. M. Čoban and K. Nagami, On monotonic generalizations of Moore spaces, čech-complete spaces and p-spaces, to appear.
- [17] E. K. van Douwen, A productive, open-and closed-hereditary invariant of $T_1$-spaces which is not hereditary, Nieuw Arch. Wisk. 19 (1971), pp. 220-221.
- [18] R. Engelking, Outline of General Topology, Amsterdam 1968.
- [19] M. E. Estill, Concerning abstract spaces, Duke Math. J. 17 (1950), pp. 317-327.
- [20] Z. Frolik, The topological product of countably compact spaces, Czech. Math. J. 10 (1960), pp. 329-338.
- [21] Z. Frolik, Generalizations of the Os-property of complete metric spaces, Czech. Math. J. 10 (1960), pp. 359-379.
- [22] Z. Frolik, Baire spaces and some generalizations of complete metric spaces, Czech. Math. J. 11 (1961), pp. 237-247.
- [23] Z. Frolik, Locally topologically complete spaces, Soviet Math. Dokl. 2 (1961), pp. 355-357.
- [24] J. de Groot, Subcompactness and the Baire category theorem, Indag. Math. 25 (1963), pp. 761-767.
- [25] L. Gillman and M. Jerison, Rings of Continuous Functions, Princeton, N. J. 1960.
- [26] H. Herrlich, Ordnungsfähigkeit topologischer Bäume, Inaugural-Dissertation, Freie Universität, Berlin, 1967.
- [27] J. R. Isbell, Uniform Spaces, Math. Surveys 12, Amor. Math. Soc., Providence, R. I. 1964.
- [28] I. Juhasz, Cardinal functions in topology, Mathematical Centre Tracts 34, Mathematisch Centrum, Amsterdam 1971.
- [29] J. L. Kelley, General Topology, Princeton, N. J. 1955.
- [30] C. Kuratowski, Topology, Vol. 1, New York 1966.
- [31] J. L. Kelley and I. Namioka, Linear Topological Spaces, Princeton, N. J. 1963.
- [32] D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. (Rozprawy Matematyczne) 89 (1971), pp. 1-36.
- [33] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), pp. 375-376.
- [34] E. Michael, Bi-quotient maps and Cartesian products of quotient maps, Ann. Inst. Fourier, Grenoble, 18 (1968), pp. 287-302.
- [35] R. L. Moore, Foundations of Point Set Theory, AMS Colloq. Publ. 13, New York, 1932.
- [36] E. Michael and A. H. Stone, Quotients of the space of irrationals, Pacific J. Math. 28 (1969), pp. 629-633.
- [37] J. C. Oxtoby, Cartesian products of Baire spaces, Fund. Math. 49 (1961), pp. 157-166.
- [38] J. C. Oxtoby, Spaces that admit a category measure, J. Reine Angew. Math. 205 (1961), pp. 156-170.
- [39] J. C. Oxtoby, The Banach-Mazur Game and Banach Category Theorem, Contributions to the Theory of Games, Ann. Math. Studios, Number 39, pp. 159-164.
- [40] B. Pasynkov, On open mappings, Soviet Math. Dokl. 8 (1967), pp. 853-856.
- [41] C. Pixley and P. Roy, Uncompletable Moore spaces, Proc. Auburn Topology Conf., March 1969, Auburn Univ., Auburn, Alabama, pp. 75-85.
- [42] J. van der Slot, Some properties related to compactness, Thesis, Amsterdam 1968.
- [43] R. Sikorski, On the cartesian product of metric spaces, Fund. Math. 34 (1947), pp. 288-292.
- [44] R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), pp. 631-632.
- [45] G. E. Strecker and G. Viglino, Cotopology and minimal Hausdorff spaces, Proc. Amer. Math. Soc. 21 (1969), pp. 569-574.
- [46] F. D. Tall, A counterexample in the theories of compactness and of metrication, Indag. Math. 35 (1973), pp. 471-474.
- [47] A. Verbeek, Minimal cotopologies, Nieuw Arch. Wisk. 18 (1970), pp. 162-164.
- [48] N. Wedenissoff, Sur les espaces métriques complète, J. Math. Pures Appl. 9 (1930), pp. 377-381.
- [49] H. E. White, Jr., Topological spaces that are a-favorable for a player with perfect information, to appear.
- [50] H. H. Wicke, Base of countable order theory and some generalizations, Proc. of the Univ. of Houston Point Set Topology Conf., 1971, Houston, Texas.
- [51] H. H. Wicke, and J. M. Worrell, Open continuous mappings of spaces having bases of countable order, Duke Math. J. 34 (1967), pp. 255-271.
- [52] H. H. Wicke, and J. M. Worrell, Completeness of first countable Hausdorff spaces II, to appear.
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